When electrical characteristics of a target object, e.g., a semiconductor wafer, are inspected, there is used a probe device for directly inspecting the semiconductor wafer. Such a probe device includes: a vertically movable wafer chuck provided in an inspection chamber, on which the semiconductor wafer is mounted; an XY stage for moving the wafer chuck in X and Y directions; a probe card disposed above the XY stage; and an alignment mechanism for aligning the semiconductor wafer on a the wafer chuck with a plurality of probes of the probe card. The probe device performs the electrical characteristic inspection while electrically contacting chips of the semiconductor wafer and the probes by overdriving the aligned semiconductor wafer. The alignment mechanism has, e.g., a lower camera attached to the wafer chuck and an upper camera, attached to an alignment bridge, capable of moving to a portion just below the probe card.
When electrodes in the chips and the probes are brought into electrical contact with each other, a chuck top is controlled so that a uniform overdrive can be applied to all the chips. However, it is difficult to apply a uniform overdrive due to manufacturing errors of the wafer chuck or the like. Therefore, a height of the chuck top is calculated by measuring heights of five points including a center point of a semiconductor wafer surface on the chuck top and right, left, upper and lower points thereof and calculating an average value for contact positions (contact coordinates) in four quadrants obtained by dividing the semiconductor wafer surface while setting a height of the center point as the origin. Since the semiconductor wafer is vacuum-attracted on the chuck top, the semiconductor wafer surface on the chuck top can be treated as a plane along a top surface of the chuck top.
Therefore, it is crucial to measure the height of the chuck top with high precision. For example, FIGS. 4A and 4B show a principal of a conventional method for calculating a height of a chuck top in a first quadrant on a top surface of the chuck. Heights of the chuck top in a second to a fourth quadrant can also be obtained in the same sequence applied in the first quadrant.
In the conventional method, XY coordinates of three points for defining XY coordinates in the first quadrant of the chuck top are specified on an XY coordinate plane of a computer (hereinafter, referred to as “ideal coordinate plane”). Based on these specified coordinates, three points on the chuck top 1 are required as shown in FIGS. 4A and 4B. As for the top surface of the first quadrant of the chuck top 1, there is set a planar model, e.g., a plane OAB formed by a center point O of the chuck top 1 and straight lines OA and OB perpendicular to each other at the center point O as shown in FIG. 4A. Further, the origin O on the ideal coordinate plane specified by the computer coincides with the center point O of the chuck top 1, and a plane including the center point O, point a in X axis and point b in Y axis on the ideal coordinate plane is defined as a plane Oab. Points A and B on the chuck top 1, which are coordinates of an actual chuck top 1 including heights thereof, are obtained in correspondence to the points a and b specified on the ideal coordinate plane. FIG. 4B depicts a relationship between the plane OAB formed of those three points on the chuck top 1 and the plane Oab on the ideal coordinate plane.
As can be seen from FIG. 4B, when the point a (xo, O) in the X axis and the point b (O, yo) in the Y axis on the ideal coordinate plane are specified by the computer, the specified positions of the chuck top 1, which correspond to the points a and b, are led directly under the position where the height of chuck top 1 is detected. Heights of the chuck top 1 in those positions are measured, and coordinates of the points A and B corresponding to the points a and b can be obtained based on the moving distance of the chuck top 1 at this time.
Following coordinate transformation formulas are used for calculating arbitrary coordinates specified on the ideal coordinate plane and heights of the chuck top 1 which correspond thereto. In the coordinate transformation formulas, contact coordinates X and Y are obtained as a function of specified coordinates x and y, and a coordinate Z is obtained as a function of the coordinates X and Y. Moreover, in the following coordinate transformation formulas, one point on the plane Oab of the ideal coordinate plane is defined as a point p (x, y), and one point on the plane OAB of the chuck top 1 which correspond to the point p is defined as a point P (X, Y, Z).X=ax+by Y=cx+dy Z=eX+fY 
Each of the coefficients in the coordinate transformation formulas is calculated by substituting the specified coordinates on the ideal coordinate plane and the measurement values of the chuck top 1 which correspond thereto. After the calculation of the coefficients, arbitrary contact coordinates x and y are specified by the computer and the coordinates are substituted to the coordinate transformation formulas in the computer. As a result, the contact coordinates X and Y of the chuck top 1 which correspond to the specified contact coordinates are obtained, and the contact coordinate Z, i.e., the height Z of the chuck top 1, is calculated based on the coordinates X and Y.a=XA/xO b=XB/yO c=YA/xO d=YB/yO e=(YB*ZA−YA*ZB)/(XA*YB−XB*YA)f=−−(XB*ZA−XA*ZB)/(XA*YB−XB*YA)
Japanese Patent Publication No. H07-105414 discloses therein a technique for making an electrical contact between a semiconductor wafer and a probe under a uniform pressure. Further, Japanese Patent No. 2986141 discloses therein a technique capable of performing alignment between chips and probes with high precision.
However, in the conventional method for calculating a height of a chuck top, it is assumed that the top surface of the chuck top 1 is a plane on the computer. With this assumption, a height of the chuck top 1 is obtained, on average, based on the specified coordinates x and y. Therefore, as the contact positions of the probes keep away from the measured points, the difference between the actual height of the chuck top 1 and the contact coordinate Z calculated based on the measured points increases. Accordingly, a variation in the contact positions increases, and especially a variation in a direction of 45° with respect to the straight lines OA and OB increases to the most. As a result, even if the chuck top 1 is overdriven in that portion, the reliability of the inspection is not ensured.